Method for Estimating Absorption Parameter Q(T)

ABSTRACT

A method and apparatus for a method for generating an estimated value of absorption parameter Q(t). In one embodiment, the method includes receiving an input seismic trace, applying a time variant Fourier transform to the input seismic trace to generate a time variant amplitude spectrum of the input seismic trace, dividing the natural logarithm of the time variant amplitude spectrum by −πf, and performing a power series approximation to the result with an index starting from one to generate an estimated value of R(t). R(t) is a ratio between traveltime t and the absorption parameter Q(t). The method further includes dividing t by R(t) to generate the estimated value of the absorption parameter Q(t).

BACKGROUND OF THE INVENTION

1. Field of the Invention

One or more embodiments of the present invention generally relate toseismic data processing, and more particularly to estimating absorptionparameter Q.

2. Description of the Related Art

Absorption parameter Q, which may also be referred to as anelasticattenuation or seismic quality factor, has considerable impact onsurface seismic reflection data. For example, preferential attenuationof high frequencies generally increases the dominant signal wavelengthand period, which therefore degrades resolution. Quantitative analysisof amplitudes is commonly complicated by absorption parameter Q duringamplitude variation with offset (AVO) analysis where attenuation effectsare superimposed on AVO signatures. If accurate values of absorptionparameter Q are known, these difficulties can be corrected. Furthermore,absorption parameter Q is a useful parameter in its own right because itis sensitive to parameters such as lithology, porosity, and pore fluidcharacteristics.

Accordingly, knowledge of Q is very desirable; however, it is rarelymeasured. Many laboratory-based measurements of Q and its dependence onparameters such as lithology and gas saturation have been made on coresamples. Unfortunately, these measurements are made usingkilohertz-range seismic signals at a limited range of ambient pressureand temperature. As a result, these laboratory laboratory-basedmeasurements, when compared to in-situ conditions, may be questionableor ambiguous.

Therefore, a need exists in the art for an improved method forgenerating an estimated value of absorption parameter Q.

SUMMARY OF THE INVENTION

One or more embodiments of the invention are directed to a method forgenerating an estimated value of absorption parameter Q(t). In oneembodiment, the method includes receiving an input seismic trace,creating at by Q gather using the input seismic trace, where trepresents traveltime. The t by Q gather has traveltime as the verticalaxis and a ratio of the traveltime and the absorption parameter as thehorizontal axis. The method further includes identifying two or moredesired features in the t by Q gather by two or more identifiers,connecting the identifiers to determine an R(t), and dividing thetraveltime by the R(t) to generate the estimated value of the absorptionparameter Q(t).

In another embodiment, the method includes receiving the input seismictrace, filtering the input seismic trace using an amplitude correctionfilter expressed as A_(R)(f)=exp(sgn πfR) and a phase correction filterexpressed as

${\phi_{R}(f)} = {{sgn}\; 2\; f\; {\ln \left( \frac{f_{\max}}{f} \right)}R}$

to generate a plurality of filtered input seismic traces in the timedomain, where f represents the frequency of the input seismic trace,f_(max) represents the maximum frequency of the input seismic trace, andR represents a ratio between traveltime and absorption parameter. Themethod further includes identifying two or more desired features in thefiltered input seismic traces in the time domain by two or moreidentifiers, connecting the identifiers to determine an R(t), anddividing the traveltime by the R(t) to generate the estimated value ofthe absorption parameter Q(t).

In yet another embodiment, the method includes receiving an inputseismic trace, applying a time variant Fourier transform to the inputseismic trace to generate a time variant amplitude spectrum of the inputseismic trace, dividing the natural logarithm of the time variantamplitude spectrum by −πf, and performing a power series approximationto the result with an index starting from one to generate an estimatedvalue of R(t). R(t) is a ratio between traveltime t and the absorptionparameter Q(t). The method further includes dividing t by R(t) togenerate the estimated value of the absorption parameter Q(t).

BRIEF DESCRIPTION OF THE DRAWINGS

So that the manner in which the above recited features of the presentinvention can be understood in detail, a more particular description ofthe invention, briefly summarized above, may be had by reference toembodiments, some of which are illustrated in the appended drawings. Itis to be noted, however, that the appended drawings illustrate onlytypical embodiments of this invention and are therefore not to beconsidered limiting of its scope, for the invention may admit to otherequally effective embodiments.

FIG. 1 illustrates a schematic view of marine seismic surveying forwhich various embodiments of the invention may be used.

FIG. 2 illustrates a method for correcting an input seismic trace fromdissipative effects in accordance with one embodiment of the invention.

FIG. 3 illustrates a method for correcting an input seismic trace fromdissipative effects in accordance with another embodiment of theinvention.

FIG. 4A illustrates t by Q gather in accordance with one embodiment ofthe invention.

FIG. 4B illustrates t by Q gather in accordance with another embodimentof the invention.

FIG. 5 illustrates a flow diagram of a method for generating anestimated value of Q(t) in accordance with one embodiment of theinvention.

FIG. 6 illustrates a flow diagram of a method for generating anestimated value of Q(t) in accordance with another embodiment of theinvention.

FIG. 7 illustrates a computer network, into which embodiments of theinvention may be implemented.

DETAILED DESCRIPTION

One or more embodiments of the invention may be used in connection withvarious seismic surveying, such as marine seismic surveying, landseismic surveying, seabed seismic surveying, bore hole seismic surveyingand the like. FIG. 1 illustrates a schematic view of marine seismicsurveying 100 for which various embodiments of the invention may beused. Subterranean formations to be explored, such as 102 and 104, liebelow a body of water 106. Seismic energy sources 108 and seismicreceivers 110 are positioned in the body of water 106, typically by oneor more seismic vessels (not shown). A seismic source 108, such as anair gun, creates seismic waves in the body of water 106 and a portion ofthe seismic waves travels downward through the water toward thesubterranean formations 102 and 104 beneath the body of water 106. Whenthe seismic waves reach a seismic reflector, a portion of the seismicwaves reflects upward and a portion of the seismic waves continuesdownward. The seismic reflector can be the water bottom 112 or one ofthe interfaces between subterranean formation, such as interface 114between formations 102 and 104. When the reflected waves travelingupward reach the water/air interface at the water surface 116, amajority portion of the waves reflects downward again. Continuing inthis fashion, seismic waves can reflect multiple times between upwardreflectors, such as the water bottom 112 or formation interface 114, andthe downward reflector at the water surface 116 above. Each time thereflected waves propagate past the position of a seismic receiver 110,the receiver 110 senses the reflected waves and generates representativeseismic signals. These seismic signals may then be used to yieldvaluable information regarding the geophysical characteristics of theexplored subterranean formations.

FIG. 2 illustrates a method 200 for correcting an input seismic tracefrom dissipative effects in accordance with one embodiment of theinvention. Steps 210 through 249 are directed toward creating at by Qgather, which is defined by an R axis and at axis, where R=t/Q, and trepresents traveltime. Q represents absorption parameter and may oftenbe referred to as the seismic quality factor. Q may also be a functionof traveltime t and as such be referred to as Q(t). At step 210, aninput seismic trace and an absorption parameter Q(t) are received. Theabsorption parameter Q(t) may be retrieved from a table stored in a database. In one embodiment, the absorption parameter Q(t) may be a range ofabsorption parameter Q(t) values, which includes minimum and maximumQ(t) values. In yet another embodiment, the absorption parameter Q(t)value may be determined using method 500 or method 600, as describedbelow with reference to FIGS. 5 and 6.

At step 220, a sampling interval along the R axis, ΔR, is calculatedaccording to

$\begin{matrix}{{{\Delta \; R} = \frac{\pi \; }{2f_{\max}}},} & \left( {{Equation}\mspace{14mu} 1} \right)\end{matrix}$

where f_(max) represents an estimate of the maximum frequency in theinput seismic trace. For example, the sampling interval along the R axisis about 0.043 seconds for a maximum frequency of about 100 Hz. In oneembodiment, the largest sampling interval for which the t by Q gather isnot aliased is selected.

Equation 1 may be derived by analyzing a phase correction filter

$\begin{matrix}{{{\phi_{R}(f)} = {{sgn}\; 2\; f\; {\ln \left( \frac{f_{c}}{f} \right)}R}},} & \left( {{Equation}\mspace{14mu} 2} \right)\end{matrix}$

where R=t/Q, f represents the frequency of the input seismic trace inthe frequency domain, f_(c) represents the cutoff frequency of the inputseismic trace, sgn=−1 when the filters are used for modeling absorptionand sgn=1 when the filters are used for compensation (i.e., inverseQ-filtering). The maximum frequency f_(max) of the input seismic tracemay be introduced into Equation 2 to distinguish the effect of thecutoff frequency f_(c) as a simple time variant time shift, which may beexpressed as:

$\begin{matrix}\begin{matrix}{{\phi_{R}(f)} = {{sgn}\; 2\; f\; {\ln \left( {\frac{f_{c}}{f}\frac{f_{\max}}{f_{\max}}} \right)}R}} \\{= {{{sgn}\; 2\; f\; {\ln \left( \frac{f_{\max}}{f} \right)}R} + {{sgn}\; 2\; f\; {\ln \left( \frac{f_{c}}{f_{\max}} \right)}{R.}}}}\end{matrix} & \left( {{Equation}\mspace{14mu} 3} \right)\end{matrix}$

The R value in the first portion of Equation 3 for which the phasereaches the value of 2π the first time is determined. It is observedthat this R value is the wavelength along the R axis of the periodiccomplex valued function e^(jφ) ^(R) ^((f)) and may be expressed as:

$\begin{matrix}{{\lambda (f)} = \frac{\pi}{f\; {\ln \left( \frac{f\; \max}{f} \right)}}} & \left( {{Equation}\mspace{14mu} 4} \right)\end{matrix}$

The corresponding frequency along the R axis f_(R)(f) may be expressedas:

$\begin{matrix}{{f_{R}(f)} = {\frac{1}{\pi}f\; \ln \; \left( \frac{f_{c}}{f} \right)}} & \left( {{Equation}\mspace{14mu} 5} \right)\end{matrix}$

Equation 5 is then solved for the maximum value of the frequency alongthe R axis as a function of the temporal frequencies between zero andf_(max). The maximum value of the R frequencies may be used to definethe sampling interval ΔR, which may be represented as:

$\begin{matrix}{{\Delta \; R} = \frac{1}{2\; {\max_{f}\left( {\frac{1}{\pi}f\; {\ln \left( \frac{f_{\max}}{f} \right)}} \right)}}} & \left( {{Equation}\mspace{14mu} 6} \right)\end{matrix}$

The temporal frequency at which Equation 5 reaches its maximum value maybe estimated as:

$\begin{matrix}{\overset{\Cap}{f} = {^{({{\ln {(f_{\max})}} - 1})} = \frac{f_{\max}}{}}} & \left( {{Equation}\mspace{14mu} 7} \right)\end{matrix}$

Accordingly, substituting Equation 7 into Equation 6 leads to

${\Delta \; R} = {\frac{\pi \; }{2f_{\max}}.}$

At step 230, a plurality of R values are determined using t, Q(t) andthe sampling interval ΔR. In one embodiment, n+1 R values aredetermined, where

${R_{\min} = {\min \left( \frac{t}{Q(t)} \right)}},{R_{\max} = {\max \left( \frac{t}{Q(t)} \right)}},{and}$R_(i) = R_(min) + (1 − i)Δ R.

At step 240, the input seismic trace is filtered using an amplitudecorrection filter A_(R)(f)=exp(sgnπfR), the phase correction filter

${{\phi_{R}(f)} = {{sgn}\; 2\; f\; {\ln \left( \frac{f_{\max}}{f} \right)}R}},$

and the R values generated at step 230, where f represents the frequencyof the input seismic trace, f_(max) represents the maximum frequency ofthe input seismic trace, sgn=−1 when the filters are used for modelingabsorption and sgn=1 when the filters are used for compensation (i.e.,inverse Q filtering). In one embodiment, the input seismic trace may befiltered using the above mentioned amplitude and phase correctionfilters by first transforming the input seismic trace to the frequencydomain (step 242). In one embodiment, the input seismic trace istransformed using a fast Fourier transform. Then, at step 244, theamplitude and phase correction filters are computed using the first Rvalue. At step 246, the result of step 244 is multiplied with the inputseismic trace in the frequency domain. In one embodiment, the result ismultiplied with the complex numbers of the input seismic trace in thefrequency domain. The result of step 244 may be capped by a maximumvalue. At step 248, a determination is made as to whether another Rvalue from the n+1 R values generated at step 230 needs to be processed.If the answer is in the affirmative, processing returns to step 244. Inthis manner, processing continues until all of the n+1 R values havebeen processed through steps 244-248, thereby generating an n+1 filteredinput seismic traces in the frequency domain. In this manner, the inputseismic trace may be filtered in the frequency domain. At step 249, then+1 filtered input seismic traces are transformed to the time domain,thereby generating an n+1 filtered input seismic traces in the timedomain, which make up the t by Q gather. In one embodiment, thetransformation to the time domain is performed using an inverse fastFourier transform.

At step 250, an interpolation algorithm is applied to the t by Q gatheralong an R(t) curve to derive a corrected input seismic trace, whereR(t)=t/Q(t). The interpolation algorithm used in step 250 may be alinear interpolation or any other interpolation algorithm commonly knownby those skilled in the art. The application of the interpolationalgorithm may also be known as “slicing through” the t by Q gather alongthe R(t) curve. Steps 210 through 250 may be repeated for other inputseismic traces. In this manner, the corrected input seismic trace may bederived by taking for each time sample of the filtered input seismictrace, the corresponding time sample from the filtered input seismictraces closest to the R(t) curve.

FIG. 4A illustrates at by Q gather 400 in accordance with one embodimentof the invention. The t by Q gather 400 is comprised within a horizontalaxis of R and a vertical axis of traveltime t. The t by Q gather is madeup of n+1 filtered input seismic traces 410. The first filtered inputseismic trace 410 is generated using the R_(min) and the last filteredinput seismic trace 410 is generated using R_(max). The t by Q gatheralso includes an R(t) curve 420 intersecting the n+1 filtered inputseismic traces 410. The t by Q gather may be sliced through along theR(t) curve 420 to generate the corrected input seismic trace.

In an embodiment in which the cutoff frequency f_(c) is not the same asthe maximum frequency f_(max), the t by Q gather may be “sliced through”an R′(t) curve, which may be expressed as R′(t)=R(t)+sgn τ(R(t)), wheresgn τ (R(t)) is derived from

${{\tau (R)} = {{sgn}\; \frac{1}{\pi}{\ln \left( \frac{f_{c}}{f_{\max}} \right)}R}},$

which is the equivalent to the time shift portion of Equation 3. Anexample of an R′(t) curve 460 with respect to an R(t) curve 420 isillustrated in FIG. 4B. As illustrated, R′(t) curve 460 differs fromR(t) curve 420 by a time shift of sgn τ (R(t)).

FIG. 3 illustrates a method 300 for correcting an input seismic tracefrom dissipative effects in accordance with another embodiment of theinvention. Steps 310 through 330 perform the same steps as steps 210through 230. Accordingly, details of steps 310 through 330 may be foundwith reference to steps 210 through 230. At step 340, the input seismictrace is filtered using an amplitude correction filterA_(R)(f)=exp(sgnπfR), a phase correction filter

${{\phi_{R}(f)} = {{sgn}\; 2\; f\; {\ln \left( \frac{f\; \max}{f} \right)}R}},$

and the R values generated at step 330. In one embodiment, the inputseismic trace may be filtered by first applying an inverse Fouriertransform to the amplitude and phase correction filters for all R values(step 342). In this manner, the amplitude and phase correction filtersare transformed to the time domain. At step 344, the result of step 342is convolved with the input seismic trace to generate the n+1 filteredinput seismic traces in the time domain, which make up the t by Qgather. The input seismic trace may also be filtered with other types ofconvolution filters commonly known by persons with ordinary skill in theart. At step 350, an interpolation algorithm is applied to the t by Qgather along the R(t) curve to derive a corrected input seismic trace.Step 350 performs the same step as step 250. Accordingly, details ofstep 350 may be found with reference step 250.

FIG. 5 illustrates a flow diagram of a method 500 for generating anestimated value of Q(t) in accordance with one embodiment of theinvention. Steps 510 through 540 are directed toward creating at by Qgather. At step 510, an input seismic trace is received. At step 520, asampling interval along the R axis, ΔR, is calculated according to

${\Delta \; R} = {\frac{\pi \; e}{2f_{\max}}.}$

At step 530, a plurality of R values are determined using t, thesampling interval ΔR, and a range of Q(t) values, e.g., minimum andmaximum Q(t) values, for a desired subterranean region. Steps 510through 530 are the same as steps 210 through 230 except that thetypical range of Q(t) values for the desired subterranean region is usedto calculate the R values, as opposed to a single Q(t) value.Accordingly, details of steps 510 through 530 may be found withreference steps 210 through 230.

At step 540, the input seismic trace is filtered using an amplitudecorrection filter A_(R)(f)exp(sgnπfR), a phase correction filter

${{\phi_{R}(f)} = {{sgn}\; 2\; f\; {\ln \left( \frac{f_{\max}}{f} \right)}R}},$

and the R values generated at step 530. The input seismic trace may befiltered using the fast Fourier transform, as described in method 200,or the convolution algorithm, as described in method 400. At the end ofstep 540, an n+1 filtered input seismic traces in the time domain aregenerated to create the t by Q gather. Steps 510 through 540 may berepeated to generate a plurality of t by Q gathers.

At step 550, the t by Q gather is displayed on a display medium, such asa screen or a visualization center. At step 560, two or more desiredfeatures in the t by Q gather are identified. The desired features maybe identified using markers or other identifiers. At step 570, thedesired markers are connected to generate an R(t) curve. The desiredmarkers may be connected by a linear line, or any other curve fittingalgorithm commonly known by persons with ordinary skill in the art. Atstep 580, the Q(t) is determined by dividing the traveltime t by R(t).

FIG. 6 illustrates a flow diagram of a method 600 for generating anestimated value of a time variant Q(t) in accordance with anotherembodiment of the invention. At step 610, a one dimensional inputseismic trace, i.e., based on traveltime t, is received. At step 620, atime variant Fourier transform is applied to the input seismic trace togenerate a time variant amplitude spectrum of the input seismic trace,which may be represented as X(t, f). The time variant amplitude spectrumof the input seismic trace X(t, f) may be expressed as:

X(t,f)=A(t,f)W(f)I(f)  (Equation 8),

where A(t, f) represents a time variant exponential absorption term,W(f) represents a time invariant source wavelet, and I(f) represents atime-invariant reflectivity. The time variant exponential absorptionterm A(t, f) may be expressed as:

A(t,f)=exp(−πfR(t))  (Equation 9),

where

${R(t)} = {\frac{t}{Q(t)}.}$

At step 630, the natural logarithm of the time variant amplitudespectrum of the input seismic trace X(t, f) is calculated and the resultis divided by −πf. Step 630 may be expressed as:

$\begin{matrix}{{S\left( {t,f} \right)} = {\frac{\ln \left( {X\left( {t,f} \right)} \right)}{{- \pi}\; f} = {{R(t)} + {{c(f)}.}}}} & \left( {{Equation}\mspace{14mu} 10} \right)\end{matrix}$

At step 640, a least squares power series approximation to S(t, f) isperformed to generate a plurality of power series coefficients s_(i),i.e., s₀, s₁, s₂, . . . s_(n). The least squares estimate to the powerseries coefficients may be computed by solving the followingminimization problem:

$\left. {{{S\left( {t,f} \right)} - {\sum\limits_{i = 0}^{n}{s_{i}t^{i}}}}}^{2}\rightarrow{\min.} \right.$

In one embodiment, the least squares powers series is of a low order,i.e., n is a small number, e.g., from about 2 to about 8.

S(t, f) may also be expressed as: S(t, f)=R(t)+c(f) where c(f)represents an unknown frequency dependent constant. At step 650, theunknown frequency dependent constant c(f) is set to be equal to thefirst power series coefficient s₀. At step 660, a power seriesapproximation to R(t) is determined by performing a power seriesapproximation to S(t, f) with the index starting from 1, as opposed to0, i.e., without using the first power series coefficient s₀. The powerseries approximation to R(t) may be expressed as:

${\hat{R}(t)} = {\sum\limits_{i = 1}^{n}{s_{i}{t^{i}.}}}$

In this manner, the ratio of traveltime t and time variant Q(t) may beapproximated by the power series approximation.

At step 670, the traveltime t is divided by R(t) to generate anestimated value of the time variant Q(t).

FIG. 7 illustrates a computer network 700, into which embodiments of theinvention may be implemented. The computer network 700 includes a systemcomputer 730, which may be implemented as any conventional personalcomputer or workstation, such as a UNIX-based workstation. The systemcomputer 730 is in communication with disk storage devices 729, 731, and733, which may be external hard disk storage devices. It is contemplatedthat disk storage devices 729, 731, and 733 are conventional hard diskdrives, and as such, will be implemented by way of a local area networkor by remote access. Of course, while disk storage devices 729, 731, and733 are illustrated as separate devices, a single disk storage devicemay be used to store any and all of the program instructions,measurement data, and results as desired.

In one embodiment, seismic data from hydrophones are stored in diskstorage device 731. The system computer 730 may retrieve the appropriatedata from the disk storage device 731 to perform the seismic tracescorrection method according to program instructions that correspond tothe methods described herein. The program instructions may be written ina computer programming language, such as C++, Java and the like. Theprogram instructions may be stored in a computer-readable memory, suchas program disk storage device 733. Of course, the memory medium storingthe program instructions may be of any conventional type used for thestorage of computer programs, including hard disk drives, floppy disks,CD-ROMs and other optical media, magnetic tape, and the like.

According to the preferred embodiment of the invention, the systemcomputer 730 presents output primarily onto graphics display 727, oralternatively via printer 728. The system computer 730 may store theresults of the methods described above on disk storage 729, for lateruse and further analysis. The keyboard 726 and the pointing device(e.g., a mouse, trackball, or the like) 725 may be provided with thesystem computer 730 to enable interactive operation.

The system computer 730 may be located at a data center remote from thesurvey region. The system computer 730 is in communication withhydrophones (either directly or via a recording unit, not shown), toreceive signals indicative of the reflected seismic energy. Thesesignals, after conventional formatting and other initial processing, arestored by the system computer 730 as digital data in the disk storage731 for subsequent retrieval and processing in the manner describedabove. While FIG. 7 illustrates the disk storage 731 as directlyconnected to the system computer 730, it is also contemplated that thedisk storage device 731 may be accessible through a local area networkor by remote access. Furthermore, while disk storage devices 729, 731are illustrated as separate devices for storing input seismic data andanalysis results, the disk storage devices 729, 731 may be implementedwithin a single disk drive (either together with or separately fromprogram disk storage device 733), or in any other conventional manner aswill be fully understood by one of skill in the art having reference tothis specification

While the foregoing is directed to embodiments of the present invention,other and further embodiments of the invention may be devised withoutdeparting from the basic scope thereof, and the scope thereof isdetermined by the claims that follow.

1. A method for generating an estimated value of absorption parameterQ(t), comprising: receiving an input seismic trace; creating at by Qgather using the input seismic trace, wherein t represents traveltime,and wherein the t by Q gather has traveltime as the vertical axis and aratio of the traveltime and the absorption parameter as the horizontalaxis; identifying two or more desired features in the t by Q gather bytwo or more identifiers; connecting the identifiers to determine anR(t); and dividing the traveltime by the R(t) to generate the estimatedvalue of the absorption parameter Q(t).
 2. The method of claim 1,further comprising displaying the t by 0 gather.
 3. The method of claim1, wherein creating the t by Q gather comprises receiving a range ofQ(t) values.
 4. The method of claim 1, wherein connecting theidentifiers comprises connecting the identifiers using a curve fittingalgorithm.
 5. The method of claim 1, wherein creating the t by Q gathercomprises calculating a sampling interval along the horizontal axis. 6.The method of claim 5, wherein the sampling interval is calculated usingan equation ${{\Delta \; R} = \frac{\pi \; e}{2f_{\max}}},$ whereinΔR represents the sampling interval and f_(max) represents the maximumfrequency of the input seismic trace.
 7. The method of claim 5, whereinthe sampling interval is the largest interval for which the t by Qgather is not aliased.
 8. The method of claim 5, wherein creating the tby Q gather further comprises determining a plurality of R values usingt, Q(t) and the sampling interval.
 9. The method of claim 1, whereincreating the t by Q gather comprises filtering the input seismic traceusing an amplitude correction filter expressed as A_(R)(f)=exp(sgnπfR),wherein f represents the frequency of the input seismic trace.
 10. Themethod of claim 1, wherein creating the t by Q gather comprisesfiltering the input seismic trace using a phase correction filterexpressed as${{\phi_{R}(f)} = {{sgn}\; 2\; f\; {\ln \left( \frac{f_{\max}}{f} \right)}R}},$wherein f represents the frequency of the input seismic trace andf_(max) represents the maximum frequency of the input seismic trace. 11.The method of claim 1, wherein creating the t by 0 gather comprisesfiltering the input seismic trace using an amplitude correction filterexpressed as A_(R)(f)=exp(sgnπfR) and a phase correction filterexpressed as${{\phi_{R}(f)} = {{sgn}\; 2\; f\; {\ln \left( \frac{f_{\max}}{f} \right)}R}},$wherein f represents the frequency of the input seismic trace andf_(max) represents the maximum frequency of the input seismic trace. 12.The method of claim 8, wherein creating the t by Q gather furthercomprises filtering the input seismic trace using an amplitudecorrection filter expressed as A_(R)(f)=exp(sgnπfR) and a phasecorrection filter expressed as${{\phi_{R}(f)} = {{sgn}\; 2\; f\; {\ln \left( \frac{f_{\max}}{f} \right)}R}},$wherein f represents the frequency of the input seismic trace andf_(max) represents the maximum frequency of the input seismic trace. 13.The method of claim 1, wherein creating the t by Q gather comprisestransforming the input seismic trace to a frequency domain.
 14. Themethod of claim 1, wherein creating the t by Q gather comprisestransforming the input seismic trace to a frequency domain using a fastFourier transform.
 15. The method of claim 12, wherein filtering theinput seismic trace comprises: transforming the input seismic trace to afrequency domain; computing the amplitude and phase correction filtersfor each R value; and multiplying the result with the input seismictrace in the frequency domain to generate a plurality of filtered inputseismic traces in the frequency domain.
 16. The method of claim 12,wherein filtering the input seismic trace comprises: transforming theinput seismic trace to a frequency domain; computing the amplitude andphase correction filters for each R value; and multiplying the resultwith the complex numbers of the input seismic trace in the frequencydomain to generate a plurality of filtered input seismic traces in thefrequency domain.
 17. The method of claim 15, wherein filtering theinput seismic trace further comprises transforming the filtered inputseismic traces in the frequency domain to a time domain.
 18. The methodof claim 15, wherein filtering the input seismic trace further comprisestransforming the filtered input seismic traces to a time domain using aninverse fast Fourier transform.
 19. The method of claim 17, wherein thefiltered input seismic traces in the time domain make up the t by Qgather.
 20. The method of claim 11, wherein filtering the input seismictrace comprises transforming the amplitude and phase correction filtersto a time domain.
 21. The method of claim 12, wherein filtering theinput seismic trace comprises applying an inverse Fourier transform tothe amplitude and phase correction filters for each R value.
 22. Themethod of claim 20, wherein filtering the input seismic trace furthercomprises convolving the input seismic trace with the amplitude andphase correction filters in the time domain to generate a plurality offiltered input seismic traces in the time domain.
 23. The method ofclaim 22, wherein the filtered input seismic traces in the time domainmake up the t by Q gather.
 24. A method for generating an estimatedvalue of absorption parameter Q(t), comprising: receiving the inputseismic trace; filtering the input seismic trace using an amplitudecorrection filter expressed as A_(R)(f)=exp(sgnπfR) and a phasecorrection filter expressed as${\phi_{R}(f)} = {{sgn}\; 2\; f\; {\ln \left( \frac{f_{\max}}{f} \right)}R}$to generate a plurality of filtered input seismic traces in the timedomain, wherein f represents the frequency of the input seismic trace,f_(max) represents the maximum frequency of the input seismic trace, andR represents a ratio between traveltime and absorption parameter;identifying two or more desired features in the filtered input seismictraces in the time domain by two or more identifiers; connecting theidentifiers to determine an R(t); and dividing the traveltime by theR(t) to generate the estimated value of the absorption parameter Q(t).25. The method of claim 24, further comprising displaying the filteredinput seismic traces in the time domain as a traveltime by absorptionparameter Q(t) gather.
 26. The method of claim 24, wherein filtering theinput seismic trace comprises: transforming the input seismic trace to afrequency domain; generating a plurality of filtered input seismictraces in the frequency domain; and transforming the filtered inputseismic traces in the frequency domain to the time domain.
 27. Themethod of claim 24, wherein filtering the input seismic trace comprises:transforming the amplitude and phase correction filters to the timedomain; and convolving the input seismic trace with the amplitude andphase correction filters in the time domain to generate the filteredinput seismic traces in the time domain.
 28. A method for generating anestimated value of absorption parameter Q(t), comprising: receiving aninput seismic trace; applying a time variant Fourier transform to theinput seismic trace to generate a time variant amplitude spectrum of theinput seismic trace; dividing the natural logarithm of the time variantamplitude spectrum by −πf; performing a power series approximation tothe result with an index starting from one to generate an estimatedvalue of R(t), wherein R(t) is a ratio between traveltime t and theabsorption parameter Q(t); and dividing t by R(t) to generate theestimated value of the absorption parameter Q(t).
 29. The method ofclaim 28, wherein the input seismic trace is one dimensional.
 30. Themethod of claim 28, further comprising performing a least squares powerseries approximation to the result to generate a plurality of powerseries coefficients.
 31. The method of claim 30, wherein performing thepower series approximation to the result with an index starting from oneexcludes the first power series coefficient.
 32. The method of claim 31,wherein the result is equivalent to R(t) plus c(f), wherein c(f)represents an unknown constant and equal to the first power seriescoefficient.